# nLab Sandbox

Q: You had codiscovered, early in the 1980s, some core ingredients of M-theory, like membranes. Later, in 1995, this came to be known as “M-theory”. How do you reflect on that?

Duff (00:45): Reflecting on M-theory is quite a big challenge. The story of M-theory began with the story of eleven dimensions. It was 1978, I think, when Werner Nahm pointed out, that supersymmetry places an upper limit on the dimension of spacetime, which is 11. And so in the early 80s, my colleagues and I looked to 11-dimensional supergravity as a candidate for the unified theory of the fundamental forces. That involves compactifying the 11 dimensions donw to 4. That had its problems. The theories we looked at were not phenomenologically very promising. Whether you have extra dimensions or supersymmetry, the problem still remains that Einstein’s gravity is incompatible with quantum mechanics, in the sense that the theory is not renormalizable in the the sense of conventional quantum field theory.

(01:51) So when string theory came along, in the 1984 string revolution, 11 dimensions got pushed to the sidelines, and we were told that 11 dimensions is barking up the wrong tree. But some of us thought, even then, that there is something not quite right: Why do superstrings live in 10 spacetime dimensions, if supersymmetry allows 11?

(02:27) The next major contribution was when Bergshoeff, Sezgin and Townsend discovered the 11-dimensional supermembrane. For me that was the starting point of what I would call M-theory. Because it said: Fine, strings are fundamental and live in 10 dimensions, but you have these membranes, which seem equally fundamental, living in 11 dimensions.

(02:25) My colleagues and I, Stelle, Howe and Inami were able yto show that if you wrap this 11-dimensional membrane around a circle, it looks like a 10-dimensional string, in fact that type IIA string. So for us, that is proof that membranes in 11-dimensions were part of the big picture including strings.

(03:26) However, that view was not a popular one, I have to say. The overriding view at that time was that spacetime had 10 dimensions, it was occupied by strings, which were the theory of everything, and all these other objects, these branes, were theories of nothing. That was the conventional view.

(03:50) So in the early 90s, there were sort of two communities, if you like: The string theory people were doing their thing in 10 dimensions; the membrane people were doing theirs in 11, and it wasn’t clear if we were on the same page, or what.

(04:05) And then, as you know, Edward Witten made this startling speach at the University of Southern California, where he pointed out that the five consistent string theories and 11-dimensional supergravity were not, as we previously thought, six rival theories of everything. They were six different corners in the deeper and more profound theory that he called “M-theory”.

(04:37) Now, given that we have been arguing in favour of membranes, the fact that the theory got called “M” was something of a Pyrric victory. It was saying: Well maybe membranes were not completely [inaudible to me].

(04:57) For me, anyway, it was clear that branes were just as important as strings. And Joseph Conlon, writing in a recent book on string theory, says that when he saw the paper about wrapping the brane around the 11th dimension, in the later 80s, he was shocked, because the history of the theory that he had been brought up with would not allow such a thing until 1995. So, M-theory had a strange history.

(05:32) I could summarize my research in the early 1980s as arguing for spacetime dimensions greater than 4, and for worldvolume dimensions greater than two in the late 80s, and that struggle was by far the harder of the two.

Q: Similarly in the late 80s, also the regularized quantization of the supermembrane led to the matrix model, which later on was re-discovered as D0-brane quantum mechanics, and then hailed as a contender for a definition of M-theory. How do you reflect on this curious M-theory conceivement?

(06:30) It was quite usual for discoveries that were made in the 80s to re-appear in the 90s.

(06:39) I don’t want to diminish the importance of the matrix model. It was very important. They built on earlier work – for what we would now call D0-branes – of the late 80s.

(that sentence seems to have been meant differently)

(06:59) But the matrix model itself was not all of M-theory. It was a corner of M-theory, and it told us certain interesting things. But there were interesting things about M-theory that it didn’t tell us.

(07:12) So I think we are still looking, in fact, for what M-theory really is. We have a patchwork picture. We understand various corners. But the overarching big picture of M-theory is still waiting to be discovered, in my view.

Q: In your famous review “M-Theory (The theory formerly known as strings)”, in the concluding section, you wrote: “The overriding problem in super-unification, in the coming years, will be to take the Mystery out of M-theory, while keeping the Magic and the Membrane.” What do you think is the status of this “overriding problem” today?

(08:08) It’s still there, of course.

(08:13) M-theory in 1995 was very promising, and it taught us a lot about the fundamental interactions. But the final theory is still not with us.

(08:24) My view, and I consistently held this view since I first started in quantum [inaudible word (gravity?)] is that we have to take a long-term stance. There’ll be no overnight miracles. We have to keep beavering away, chipping away, and hopefully, one day, we’ll find the answers.

(08:48) I am optimistic that there is an M-theory without nagging mystery, but I would not like to put a time-scale on how long it would take us to find it.

(09:01) My argument would be for patience. This is what we need right now. Of course that’s not popular with the journalists, critics (?) or (?) gravitification.

(09:16) But if we look at the discussions that had the greatest impacts, recently: the Higgs boson took 50 years between its prediction and its discovery; the cosmological constant, if indeed that’s what dark energy is, would be a hundred years between the prediction and the discovery; similarly gravitational waves.

(09:42) So there is no reason to think that a Theory of Everything is going to come along any quicker than these other discoveries. We just have to keep hoping for the best.

Q; In the late 90s you wrote in Scientific American and also in your book on M-theory: Future historians may judge the late 20th century as a time when theorists were like children playing on the sea shore, diverting themselves with the smoother pebbles or prettier shells of superstrings, while the great ocean of M-theory lay undiscovered before them.“ How do you look at his prediction 20 years into the 21st century?

(10:30) I hope you recognize that most of these words were of Isaac Newton, I just made a few substitutions in the right places.

(10:40) I still hold the view that perturbative 10-dimensional strings, as they were persued in the late 80s, will be seen to be a small corner of the final theory.

(10:57) That’s not a view that’s necessarily shared by others. Ed Witten, in fact, wrote to me, after I wrote that, to argue that he didn’t share that view.

(11:10) There is a certain faction that belives that strings are more fundamental that branes because string theory admits a perturbation expansion.

(11:23) But in my view, that’s not the criterion for what is fundamental and what isn’t.

(11:29) [inaudible word] does not do perturbation theory, perturbation theory is what we do because we don’t know any better.

(11:38) So the fact that branes do not admit a perturbative treatment, as strings do, is not, in my view, a reason for thinking that branes are less fundamental than strings – especially since strings are just a limiting case, as we see, of branes.

(11:58) I don’t see how you can maintain that one object which is not fundamental has a limiting case which is.

(12:08) So we have to treat them democratically.

Q: In your interview by Farmelo, last year, you said: “The problem we face is that we have a patchworks understanding of M-theory, like a quilt: We understand this corner and that corner, but what’s lacking is the overarching big picture. Directly or indirectly, my research hopes to explain what M-theory really is. We don’t know what it is.” Do you have a hunch what form the answer might eventually take?

(12:44) No, actually I don’t know. I wouldn’t like to predict what the ultimate picture of M-theory will be. I imagine it will be something quite different from what we can imagine now.

(12:58) Going back to how the M-theory has developed: One curious feature of the big story is the AdS/CFT correspondence. Because when Maldacena wrote his paper, he had three examples: $AdS_4 \times S^7$, $AdS_5 \times S^5$, $AdS_7 \times S^4$. Two of those were 11-dimensional M-theory compactifications and the other one was type IIB.

(13:33) But if you look at the papers that have been written since Maldacena’s seminal contribution, the vast majority of them have been on the $AdS_5 \times S^5$-story.

(13:47) For whatever reason there hasn’t been the same progress in M-theory, as a result of that.

(13:58) The AdS/CFT correspondence in a way diverted attention away from the goal of finding a unified theory of all the fundamental forces, starting from 11 dimensions.

(14:13) It’s been tremendously succesful in its own right, Maldacena’s paper is the most highly cited paper in history. But it has not, strangely enough, contributed to how we unify the strong, weak and electromagnetic forces with gravity. At least I don’t think it has. That’s a different problem. I would have been happier, I think, looking back, if we were further down that road, since 1995, than we are.

(14:48) But I am still optimistic that we are on the right track.

Q: So you believe we ought to get back to the original big question about what’s the nature of M-theory.

(15:03) That’s my view, yes.

$\ldots$

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Last revised on January 23, 2020 at 13:49:45. See the history of this page for a list of all contributions to it.